Supported Distributions

R2026b

Statistics and Machine Learning Toolbox™ supports various probability distributions, including parametric, nonparametric, continuous, and discrete distributions. The following tables list the supported probability distributions and supported ways to work with each distribution. For more information, see Working with Probability Distributions.

For a custom probability distribution, use a custom distribution template to create a probability object and then use the Distribution Fitter app or probability object functions. For details, see Define Custom Distributions Using the Distribution Fitter App. You can also define a custom distribution using a function handle and use the mle function to find maximum likelihood estimates. For an example, see Fit Custom Distributions.

Continuous Distributions (Data)

Distribution	Distribution Object	Apps and Tools	Distribution-Specific Functions	Generic Functions
Beta	`BetaDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`betapdf` `betacdf` `betainv` `betastat` `betafit` `betalike` `betarnd`	`pdf` `cdf` `icdf` `random` `mle`
Birnbaum-Saunders	`BirnbaumSaundersDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Burr Type XII	`BurrDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	—	`pdf` `cdf` `icdf` `random` `mle`
Exponential	`ExponentialDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`exppdf` `expcdf` `expinv` `expstat` `expfit` `explike` `exprnd`	`pdf` `cdf` `icdf` `random` `mle`
Empirical Distribution	`EmpiricalDistribution`		`ecdf` `ecdfhist`
Extreme value	`ExtremeValueDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`evpdf` `evcdf` `evinv` `evstat` `evfit` `evlike` `evrnd`	`pdf` `cdf` `icdf` `random` `mle`
Gamma	`GammaDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`gampdf` `gamcdf` `gaminv` `gamstat` `gamfit` `gamlike` `gamrnd` `randg`	`pdf` `cdf` `icdf` `random` `mle`
Generalized extreme value	`GeneralizedExtremeValueDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`gevpdf` `gevcdf` `gevinv` `gevstat` `gevfit` `gevlike` `gevrnd`	`pdf` `cdf` `icdf` `random` `mle`
Generalized Pareto	`GeneralizedParetoDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`gppdf` `gpcdf` `gpinv` `gpstat` `gpfit` `gplike` `gprnd`	`pdf` `cdf` `icdf` `random` `mle`
Half-Normal	`HalfNormalDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	—	`pdf` `cdf` `icdf` `random` `mle`
Inverse Gaussian	`InverseGaussianDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Logistic	`LogisticDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Loglogistic	`LoglogisticDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Lognormal	`LognormalDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`lognpdf` `logncdf` `logninv` `lognstat` `lognfit` `lognlike` `lognrnd`	`pdf` `cdf` `icdf` `random` `mle`
Loguniform	`LoguniformDistribution`	—	—	`pdf` `cdf` `icdf` `random`
Nakagami	`NakagamiDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Normal (Gaussian)	`NormalDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`normpdf` `normcdf` `norminv` `normstat` `normfit` `normlike` `normrnd`	`pdf` `cdf` `icdf` `random` `mle`
Piecewise linear	`PiecewiseLinearDistribution`	—	—	—
Rayleigh	`RayleighDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`raylpdf` `raylcdf` `raylinv` `raylstat` `raylfit` `raylrnd`	`pdf` `cdf` `icdf` `random` `mle`
Rician	`RicianDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Shifted (two-parameter) exponential	`ShiftedExponentialDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random`
Shifted (three-parameter) gamma	`ShiftedGammaDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random`
Shifted (three-parameter) Weibull	`ShiftedWeibullDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random`
Stable	`StableDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Triangular	`TriangularDistribution`	—	—	—
Uniform (continuous)	`UniformDistribution`	Probability Distribution Function Tool Random Number Generation Tool	`unifpdf` `unifcdf` `unifinv` `unifstat` `unifit` `unifrnd`	`pdf` `cdf` `icdf` `random` `mle`
Weibull	`WeibullDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`wblpdf` `wblcdf` `wblinv` `wblstat` `wblfit` `wbllike` `wblrnd`	`pdf` `cdf` `icdf` `random` `mle`

Continuous Distributions (Statistics)

Distribution	Distribution Object	Apps and Tools	Distribution-Specific Functions	Generic Functions
Chi-square	—	Probability Distribution Function Tool Random Number Generation Tool	`chi2pdf` `chi2cdf` `chi2inv` `chi2stat` `chi2rnd`	`pdf` `cdf` `icdf` `random`
F	—	Probability Distribution Function Tool Random Number Generation Tool	`fpdf` `fcdf` `finv` `fstat` `frnd`	`pdf` `cdf` `icdf` `random`
Noncentral chi-square	—	Probability Distribution Function Tool Random Number Generation Tool	`ncx2pdf` `ncx2cdf` `ncx2inv` `ncx2stat` `ncx2rnd`	`pdf` `cdf` `icdf` `random`
Noncentral F	—	Probability Distribution Function Tool Random Number Generation Tool	`ncfpdf` `ncfcdf` `ncfinv` `ncfstat` `ncfrnd`	`pdf` `cdf` `icdf` `random`
Noncentral t	—	Probability Distribution Function Tool Random Number Generation Tool	`nctpdf` `nctcdf` `nctinv` `nctstat` `nctrnd`	`pdf` `cdf` `icdf` `random`
Student's t	—	Probability Distribution Function Tool Random Number Generation Tool	`tpdf` `tcdf` `tinv` `tstat` `trnd`	`pdf` `cdf` `icdf` `random`
t location-scale	`tLocationScaleDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`

Discrete Distributions

Distribution	Distribution Objects	Apps and Tools	Distribution-Specific Functions	Generic Functions
Binomial	`BinomialDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`binopdf` `binocdf` `binoinv` `binostat` `binofit` `binornd`	`pdf` `cdf` `icdf` `random` `mle`
Bernoulli	—	—	—	`mle`
Geometric	—	Probability Distribution Function Tool Random Number Generation Tool	`geopdf` `geocdf` `geoinv` `geostat` `mle` `geornd`	`pdf` `cdf` `icdf` `random` `mle`
Hypergeometric	—	Probability Distribution Function Tool Random Number Generation Tool	`hygepdf` `hygecdf` `hygeinv` `hygestat` `hygernd`	`pdf` `cdf` `icdf` `random` `mle`
Multinomial	`MultinomialDistribution`	—	`mnpdf` `mnrnd`	—
Negative binomial	`NegativeBinomialDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`nbinpdf` `nbincdf` `nbininv` `nbinstat` `nbinfit` `nbinrnd`	`pdf` `cdf` `icdf` `random` `mle`
Poisson	`PoissonDistribution`	Distribution Fitter Probability Distribution Function Tool Random Number Generation Tool	`poisspdf` `poisscdf` `poissinv` `poisstat` `poissfit` `poissrnd`	`pdf` `cdf` `icdf` `random` `mle`
Uniform (discrete)	—	Probability Distribution Function Tool Random Number Generation Tool	`unidpdf` `unidcdf` `unidinv` `unidstat` `unidrnd`	`pdf` `cdf` `icdf` `random` `mle`

Multivariate Distributions

Distribution	Distribution Object	Distribution-Specific Functions
Copula (Gaussian copula, t copula, Clayton copula, Frank copula, Gumbel copula)	—	`copulapdf` `copulacdf` `copulaparam` `copulastat` `copulafit` `copularnd`
Gaussian Mixture	`gmdistribution`	`fitgmdist` `pdf` `cdf` `random`
Inverse Wishart	—	`iwishrnd`
Multinomial	`MultinomialDistribution`	`mnpdf` `mnrnd`
Multivariate normal	—	`mvnpdf` `mvncdf` `mvnrnd`
Multivariate t	—	`mvtpdf` `mvtcdf` `mvtrnd`
Wishart	—	`wishrnd`

Nonparametric Distributions

Distribution	Distribution Objects	Apps and Tools	Distribution-Specific Functions
Kernel	`KernelDistribution`	Distribution Fitter	`ksdensity`
Pareto tails	`paretotails`	—	—
Empirical	`EmpiricalDistribution`	—	`ecdf`

Flexible Distribution Families

Distribution	Distribution Objects	Distribution-Specific Functions	Generic Functions
Pearson system	`PearsonDistribution`	`pearspdf` `pearscdf` `pearsrnd` `pearsinv`	`pdf` `cdf` `random` `icdf`
Johnson system	—	`johnsrnd`	—